Chapter 8, Problem 16SE

The article “Electrical Impedance Variation with Water Saturation in Rock” (Q. Su, Q. Feng, and Z. Shang, Geophysics, 2000:68–75) reports measurements of permeabilities (in 10^–3μm² percent), porosities (in percent), and surface area per unit volume of pore space (in 10⁴ cm^–1) for several rock samples. The results are presented in the following table, denoting In Permeability by y. porosity by x₁, and surface area per unit volume by x₂.

a.    Fit the model $y={\beta }_0+{\beta }_{1}x+{\beta }_2{x}_2+{\beta }_3{x}_1{x}_2+\epsilon$ Compute the analysis of variance table.

b.    Fit the    model $y={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_{{}^2}+\epsilon$. Compute the analysis of variance table.

c.    Fit the    model $y={\beta }_0+{\beta }_1{x}_1+\epsilon$. Compute the analysis of variance table.

d.    Compute the F statistics for comparing the models in parts (b) and (c) with the model in part (a). Which model do you prefer? Why?